Axial Compression Test of Thin Circular Cylinders. A. Length Effect. B. Visual Study of Buckling Citation Kanemitsu, Sunao and Nojima, Noble M. (1939) Axial Compression Test of Thin Circular Cylinders. A. Length Effect. B. Visual Study of Buckling. Master's thesis, California Institute of Technology. doi:10.7907/HBZ9-MZ48. https://resolver.caltech.edu/CaltechETD:etd-12052005-105325 Abstract A: This portion of the report contains results obtained from compression tests on 95 thin-walled steel circular cylinder. The tested cylinders were mainly of very small L/R ratio and large R/t ratio. The results are compared with the existing theoretical failing stresses and are also presented in a non dimensional form, δ/E. The failure stress is best given by the equation δ/E = 9(t/R) 1.6 + .16(T/L) 1.3 . This equation shall be limited for use for L/R greater than 0.1 and for L/R greater than 1.5 assume L/R = 1.5. B: A visual study of buckle formation is presented to aid future research which may be done on compression of thin cylinders. Item Type: Thesis (Master's thesis) Subject Keywords: thin circular cylinders ; (Aeronautics) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Aeronautics Thesis Availability: Public (worldwide access) Research Advisor(s): Sechler, Ernest Edwin Group: GALCIT Thesis Committee: Unknown, Unknown Defense Date: 1 January 1939 Record Number: CaltechETD:etd-12052005-105325 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-12052005-105325 DOI: 10.7907/HBZ9-MZ48 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 4791 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 06 Dec 2005 Last Modified: 16 Aug 2023 23:58 Thesis Files Preview PDF - Final Version See Usage Policy. 11MB Repository Staff Only: item control page

AXIAL COMPRESSION TEST OF THIN CI RCULAR CYLINDERS A. LENGTH EFFECT B•• VISUAL STUDY OF BUCKLING THESI S BY Suna o Kanemitsu Noble M. Nojima In Pa rtia l FulfillmentJ of the Requirements f or the Degree of Master of Science in Aerona utical Eng ineering . Calif ornia .Institute of Technology Pa s ade na , ~ Calif ornia 1939 TABLE OF CONTENTS Page 1. Acknowledgement 1 2. Definition of Symbols 2 3. Summary 3 4. Introduct ion 4 5. Historical Notes 5 6. Length Effect of Thin Circular Cylinders Under Compression 7. A. Equipment and Test Procedure 8 B. Failure of Short Specimen 10 C. Discussion of Results 11 D. Possible Applica tion t o Design 15 Buckling Wqve Pa ttern of Thin Circ ular Cylinders Under Compres s ion 17 A. Apparatus and Test Procedure 19 B. Descriptions and Comments of Buckling Process 22 c. General Discussion of Results 35 8. Figures 37 9. References 59 1 ACKlTOWLEDGEMENT~ We wish to thank Dr. E. E. Sechler and Dr. W. L. Howland for their gui dance and gene rous a i d in enabling us to present this thesis. 2 DEFI NI TION OF SYMBOLS 1 length R radius t thickness E Young's Modulus P compressive load A. area ~ Pois s on's ratio ~ compr essive stress 1!';';-t. actual failure stres s 2 !i Rt PIA cri tical compressive stress refers to critical buckling failure stres s ~ t /~)R SU:H"lv.ARY A. This portion of the r e port cont a i n s r esult s obt ained f r om compr e s sion t e s t s on 95 thin-walled steel circu l a r cylinde r~ The t e sted cylinders '>vere mainly of v ery small L/R r at io and l a r ge R/ t ratio . The result s s..re compar ed ·•;i th the exi s ting the oretical failing stresses and are also presented in a non dimensiona l form , ~/E . The f a i lure stre ss is best gi ven by t he equat ion <tjE -:::. 9 (t / R) 1 • 6 + .16(t /L) 1 • 3 • This equa tion shall be limited f or u s e for L/R great er t han 0.1 and for L/R greater than 1.5 assume L/R :. 1.5. B. A visual study of buckle : ormat ion i s uresent e d t o a id futur e res earch which ma y be done on compress ion of thin cylinders. 4. INTRODUCTION In t h e summer of 1938 a careful s tudy was rna de of a ll litera ture s pert a ining to the strength of thin wa lled cylinde rs . One ph a s e of thi s study l ead to the obv ious conclusion that there was very poor a gre ement betV!een t he theoretic a lly predicted and the experiment a lly obta i ned failing load of such cylinders particul a rily for l a r ge R/t ratios. Also it was found that very little i nforma t i on was available on the effect of length on the strength propertie s of such thin unstiffene d cylinde rs. of a ir ul an e s has grovm l ar ger ~ ithin As the size recent ye a rs the R/t r a tio of the f use l age has bec ome l a r ger without, however, an appreci able increa se in the bulkhead s na cing . It h a s been known that v ari ati on in length affe ct t h e strength pr operti e s of cylinde rs in c ompression and it i s t herefore v e r y i m~ ort ant to know defi nitely to wh at extent length influenc e s the f ai lure stress. With these t wo 0roblems i n min d the rese arch was conduc ted in t wo rar ts as following : A. Te sting of cyli nders of v ar i ous R/t ratio an d with various lengths and es pecia lly cylinde r s whose lengths were shorter than the radius . Investigating cylinders in vihich the R/t r atios were higher than has be en previ ously investigated. B. A visual study of buckling of thin cylinders by defle cting the cylinders very s lowl y . Also, recording the wave pattern at different st aye s ~ of deflection by measuring the s i z es of ouckl es , and by photograPhing the specimens. 5. HISTORICAL ]\TOTES The s t udy of thin cylinders in c owpress ion is a ve r y old problem . It was first studied experimentally by W. Fair- ba in i n 1849 . The first theoretic a l analysis of the problem was made by Lilly in 1906. A fe w years l ater, the theoret ical studi es were soon fol lowed up by a number of aut hors among whom were Timosher~o (r e fe~ence l pag e 438), Lorenz (reference 1 page 453), Sout hwell (referenc e 2), and Dean (re fere nce 3 ). The theoretica l ana l y se s wer e bas ed on cases wh ere length e f ~e ct was · negligi ble. The earliest t heoretic a l analyses were based on s ymmetrica l buc kling, f or which t he critic al stre s s bec ~me ~-~ ~ ~ • ... ·~\~ The l ater theoretic a l ana l y s es wer e ba s ed on the bending theory of t hin shells a s has been developed by Love. There are f our s olutions av a ilable: 1. Undefined t ype of buc kling , axi a l wav e lengt h s mall. s ame as s ymmetr ica l buc kling case. It is oft en referre d to as the Ti rr.oshenko or Lorenz form . 2. ~.rhen only one h a lf wave f orms in the axi a l di rection , 4 that is when ~E) > 'l.~~?l(.\-~) or anothe r words lengt h v er y short. lfl.E. ;_1. G;R. ~ \1.(\- f) L~ 3. Euler ' s f ormul a fo r ele mental strip . W hen cylinders a re very l ong and br eak up a s a strut without t he formation of buckl es . ~R-::.. 1tl.Ei R.l. 2.L'Z. Eul er' s c ollillln . 6. 4. When cylinde r s a re of infintte lengt h , and axi a l wave lengths a r e v e ry l ar ge a s compared with circumfer ent i a l wave lengths. ~ 'C. :;-~ "~R - o.<o 'J~(,- ") R... Often refered ~o a~ Southwell' s Ca s e . Th e ac c e pt e d theoretic a l equa tion f or cr it i c a l stre s s is ~ ~ <* l:. ~. ~)R. The Southwell' s c as e gives a lower va lue of stress but exueriments have shovm tha t axial wave lengths a r e equa l to or l e s s than the circumf er entia l wave l ength. Failures of Southwe ll's type a r e not obt a ined pra ctica lly. Extensive experimental Investiga tion was st a rt ed by Rober ts on (referen c e 4) in order to check the existing theoretical equation . Robertson was the one who pointed out the f act that f a ilure of Southwell ' s type di d not oc cur. He f ound that experimentally obt a ined stre ss was ve r y low compared to the theoretical failing va lue . Wi l son and Newma r k (refer ence 5), int ere sted i n cy linders as a column, inv e st i gate d the str ength of t h in cylinder, a nd likewise fo und the ac tual f a iling stres se s v er y l ow. With an intr oduction of t he stre ssed s kin t ype of airplane cons tru ct ion , t her e was r en ewe d interes t in the instability uro blem of t hin s h ells . San den a nd Tolke (reference 6 ), and Flugge(reference 7), ma de t heoreti ca l ana l yses , h owever , they have ar r ived at a simila r r esult as t hat obt a ined by earlier investigators. Re c ent l y Donnell (refer enc e 8), ha s a dv anced a new l ar ge de fl ect i on t heory c ons idering i n iti a l deforma t ion . Donnell believ es t h at t he l o~Ti e ss of the ex- perimenta l f a iling stres s was due to the f a ct t hat i t is practica lly i m9os s ibl e to ma ke a mathemat i ca l ly corr ect cylinder under ordina r y circumstances. 7. There ha s a.l so been i ntensive expe riment o.l i nv e stigation in recent year s . At the N. A.C. A., Lundquist (reference 9), has made tests on Dural, in which he compares the r es u lts with the theory and gives an equation f or f a ilu re . Donnell has made test s at GALCIT on ste e l and brass i n an a t tempt to chec k the class ical t heory an d Fl ug ge has run tests on celluloid cylinders. Hov1ev er , none of thes e exner i ments reached a higher v a lue than 60% of the t heoret ica l va l ue . Wagner and Baller sted (refer ence 10) have done experimental work on cylinders to find the length eff e ct . They ran tests on brass cylinders f or which the 1/R v a l ues were as low as .50 and the R/t values as high a s 4000, and have given an emnerical de sign formula• ~ ~ ."t \ -t ~:~ \t\~. PART A LENGTH EFFECT OF THIN-CIRCULAR CYLINDERS I N ~\XI A L COMPRESSI ON 8. EQUIPMENT AND TEST PROC~DURE The materi a l used for the s e test s was standar d shim stock steel. The test s were conducted on six d ifferent thicknesses, the nominal t h ickne ss varying from .002" to .009" , With these thicknes s the test cylinders had a R/t range from 750 to 3000, since the fabric a ted cylinders h ad a r a dius of 6.375". The thickne sses of the material were measured with an ordinary micrometer of lea s t reading 1/lOOOinch and measurements were approximated to 1/10 of this valu e. The me chanic a l properties of thes e shim stock v a ried for every thickne ss and it was nece s s ary to find t he Young 's Modulus for each thickness (table 1). The s tress s t r a in rela tion was obt a ined for the materia l in t ension in the direction in which the material was to be c ompres sed as a finished cylinder. The work wa s done in a Riehle 3000# testing machine (s e e figure 1). The stra in for the mat erial was measured with an Arne ' s dial in a s pe cia lly ba l anced frame. The stra in gage r ead dire ctly in 1/10, 000 Qnit strain and c ould cons istently be read to 1/10 of this v a l ue . The cylinde r was a tt a che d to bulkhead shown in fi gure 2, of special design with bu ilt i n cl~mp s. Th ese clamps were 1/2 inch deep, and each clamp wa s tight ened wi th a s ing le screw. These bulkheads made the cylinder fa brica tion simpl e and f a st, since no jig was requ ired . In fabric ating t he cylinder, t he shim s t ock was cut to t he leng t h of t he develoued surfac e and pl aced i n the bulkhead. To c ontrol the height of the cylinder, the edge 9. which went between the clamps was milled so that the edges were par allel and stra ight . for thi s method. Th is is very i mport ant The seam was closed by soldering a 1/ 2 inch wi de stra p over the joint. The soldering proce ss i s very important bec ause any th er mal expans ion of the sheet during the process of soldering usually l eft a buc kl e or a s oft s pot in the cylinder wall . Figure 3 shows a solde red s pecimen ready to be tested . Figure 4 shows the test auparatus with the specimen in position . The load is a pplied by the j a ck and transmitted through the ring which measures the load to the test cylinde r. The ball universal joint between the ring and t he c ylinder bulkhead transmits load only in the vertica l dire cti on. The ball cup is centered on t he centering pin built i n t he bulk- head. The test cylinder was leveled and the ca libra ted ring was aligned vertically so that di a l deflection reading was in the vertical direct i on . Load was a T~ ~ lied s lowly but continuously and only fai lure loads wer e noted . Specimens of v ery short l ength which took v er y l a r ge loads were tested in a 15000# st andar d te sting machine . 10. FAILURE OF SHORT SPECIMENS In fi gure 5 is s hown a failure picture of suecimen of v ery short length. Inve s tigation ha s shown that it is a f ailure of Eul er elemental strip with fi xed end . This t y pe of failure occurred for specimen which L/R wa s less than about .12 for R/t of 750. ratio was les s the .07. For R/t ~ 3000 the L/R Such failure occurred with a sudden collapse on steady rise in load. Figure 6 shows a failure of the cylinder with t wisting. Such fai l ure occurred for s pecimen up to L/R r a tio of .3 for t hicker m&terial and smaller L/R for t h inner material. This failure is a very intere s ting failure. It is believed tha t a s s oon as the buckl es f orm1 t he edges in the axial direction of the buc kl e s a r e unstabl e I and thus go into the form of least resistance. In this c a se the resistance of the se edges in the circumferential direc t ion is the lowest and t hus t he cylinder t wi sts . For s pecimens with L/R v a l ue from .20 to .25 the t wist was found to be a bout • 0063 ra di:an~ •. 11. DISCUSSI ON OF F~ SU LT S The experimental data ·were re duced in form of <J~"T-::. ~ The cor r es ~ onding theoretica l critica l stress c a lcula tion wer e made us ing l:.. \. <l:~' ~~\-~) R· in the ratio of ~~to These stres s es were put get a dimensionless number . Also the data were reduced to another fo rm of di men s ionless number ~ a s was used by Lundquist. Exuerimental Dat a of Donnell, Lundquist, and V!ilson and Newma rk we re taken from N. A.C. A. TR. 473 . of <r;E Lundquist has the v a lues in f orm , which we re changed over to • Wagner's test data on Brass wer e a lso r educed to form of The published dat a of Wa gner's test s do not include t h e v alue of El a stic Modul us of his mate ria l. The value of E for his test s was assumed to be 16 .0xl06#/in2 • With an assumption of "no l ength eff ect", ·the of all te sts a r e plotted ag ainst R/t in fi gur e 7. o;.,c.-r,/0;-11E.o The pre s ent t ests have ext ended cons i der abl y the r ange of inve st i gated R/t, but a l s o have inc r~a se d the sca t ter of points. A recommen ded des i gn formul a which some designers L'1b h ave be en using for dural is <l~R ~ ,la.oS t::l--R) . This is written in fo r m ~~-::.. l~ )¥.., and plott ed a s a dotted line. The ratio ~~.,.~-0 for the da t a obt ained by t he aut hors was next plotted against L/R f or a cons t ant ~/t ratio i n Figure 8 to Figure s 13 . I n t hese plots it v1as found that certain v ari ations of R/t were permissable and still have the DOints stay within t he r ange of experi menta l scat t er. For R/t of 750, such allowable var i at ion was between 700 and 12 . 800 . For R/t of 3000 , t h e allowabl e v a riat i on i n creased to a l imit be t ~e en A curve was dr awn through 26 00 to 3400 . the s e points and fi nall y c ombined on a sing l e gr aph of ~~~ ulott ed against L/R fo r a cons t ant R/t as in ~'1''*:0 ~ Figure 15 . A cro s s plot was made from f i gure 15 to get a curv e of erA~~ v e r s us R/ t for a c onstant L/R as in fi gur e ~'1''\(;Q 16 . I n orde r to plot s u ch a family of smoot~ c urves as in fi gure 1 5 and 16 , each indiv i dua l curve i n fi gur e 8 to fi gure 13 was va ried to make up a smooth fami l y satisfying the experiment a l da ta . The Euler equation f or the buckl ing stres s of an -.~r. t,~ el emental strip is ~' ~ ~(\ -~.._) L.... f or f ixe d end . Noting tha t for very short leng t hs , the fai l ure was of thi s t yue , this equation was where ~~~~ ~ut is the cri ti c a l s tres s for buc kling ; 1t~ t.R cr.,.~ ~ ~~(\-\l-~ L1.. <I't.R , in t he form of 0 ~ ~ lR\l.. l~('-~"'\ R L: J 1\-a.. This curve was expected to follow t h e experimental curve in reg i ons wher e the L/ R r atio wa s les s than . 05 from R/t r atios of 2000 , and 3000, experiment a l curve a pproaches the Euler but the experiment al a r e somewhat too low. From the ·•u bli shed dat a of t he expe rimental wor k of Donne ll , Lundqui s t , Wi l son and Newmark , and Wagne r a nd Baller s tedt , t he dat a which were wi thi n our experimental r ange of L/R and with R/ t's that a r e wi thin the allowa ble R/t v ari ation were. s .uotte d on t £1e curves . Lundquis t ' s and Wagner ' s data g ive poin t s whi ch a r e equal t o or higher than those obt a ined by the authors but are st ill wi thin the r ang e of the ex pe rimental s c atter . 13 . Donnell's te.st data are for L/R ~ 2 and fits the extended curves well. Wilson and Newmarks te s ts give consistantly lowe r values. The curves for R/t --:. 1000 and 1600 have been extended to L/R values beyond the inve s tig ated : _Joints on the strength of the se published dat a . In fi gure 14 the curve for R/t ~ the experimental data given by Wa gn er . 500 was drawn fro m Because it se ems to fit the family of curves on figure 15 very well, t ne cur ve was extended to lower L/R values and other published da ta were sootted in. for ~~~ ~,.~ This curve was not used in cross plotting versus R/t. The cylinders investigated by Lundquist were made of dural and had a radius of 7.5 inches and 15". Wagner's cy- linders were made of brass with radius of 4 and 8 inches, but as previously ment ioned , the ~la st ic Modulus is un~~own . Donnells tested ~linde rs of brass and steel for which exact dimensions are unknovm, however, they are cylinders of very small radius. Wilson and Newmark te sted cylinders of steel in whi ch the radius varied from 2 to 40 inches. Hi gh value given by Lundquist and Wagner may be due to the l a r ge cylinders although the Wilson and Newmark tests do not indi ~te that such would be expected. As mentioned earlier, there a r e 3 solutions obtainable from the thin shell bending theory . They are ~ - 1'\~E. t.~ Euler elemental strip ~a- \7-(l-~'-') L.._ 'E. <S'Q.R-::.. ~ 'I~ (' -\-L") R 1\~ l::. R.l.. '2. L~ Buckling range Euler column In fi gure 17 and 18 t hese 3 different c r itica l r anges are plotted in form of ~ versus L/R. The Eul er el emental strip equation was ~u lti ~ lied by 4 to s a t is f y the end fixity condition. Also the Euler column f ormula wa s multi plied by 4 to g ive a condition of fixed end . Theoretically, with these 3 formula s the cri tical stresses f or a ll lengths of cylinders should be predictable . In fi gure 17 and 18 it should be noted tha t scale of L/R at 1.0 is discontinuous and j umps to 100 . ~ ~~~~ f or buck- ling and experimental are constant through range of 10. The experimental curve a lso has been dra ~~ toget her with theoretical curves for the 3 regimes of failure. The experimental curve only a pproaches the theoretica l at very small and very large L/R v a lues, both ca s e s being out of the buckling r ange. At very l arge L/R va lues Southwell's case must hold but there is no way of designating such point s. 15 . POSSI BLE DESIGN APPLICATION Wagner has developed a n err.pi ri cal design for rr.ula ~ t. \ li.\~ ~ ':,. .-z.tR.l ~ ~.~ rc 1 This f ormula fi ts the exper i m en~al points very well f or an R/t value of 750 except t hat the stresses given by t he f ormula are t oo low between L/R of 0.2 and 0.5. ~It For l arge values the formula gives stresses which are too high for L/R values greater t han 0.4. A new design empirica l for mula has been developed by the aut hors on the bas is of all of t he experimental inf ormat ion avai l able, t h is formula hav ing t he sa me f orm as that of Wagner. t. The s ame variables are used ( ~ and (t/L) or ( ~ ~ ) , but the constant coeff icients and the exponent s have been a ltered. tr" The authors' f ormula is -l ~·'I "l\'·~ ~~ ~(RJ ~.Ho\1:.) The experimental values r educed t o the for m ~ has been plotted again st L/R for const ant R/t in fi gures 19 and 20. The empe ric al de s i gn formula is ca lcu l ated f or a given R/t and drawn through the points as a curve. Between L/R of 0 .1 and 1.5 a ll curves se em to fit the points fa irly well . For L/R v a l ues greater than 1.5, the L/R ratio can be a ssumed to equal 1.5 since the tests have shown t ha t ther e i s no consistant decrease in stress due to i nc rease above 1. 5 . Th i s can be best seen by analyzing Donne ll's t est resul t s in which he has investigated L/R ratio f~om 2.0 to as h igh as 32 . The question a rises with such de s ign formul a whether it can be a pplied safely t o other mat eria ls. In figu res 8 to 14 data on brass and dural are plotted . Although t hese data give cons istantly a somewhat h i gher cr itica l stress , 16 . t h e points a r e well wi thin the rang e of experimental scatt er of the da ta f or which t h e f ormul a was der i ved . 17 PART B Visual Study of the Buckling Process of Thin Circular Cvlinders 18 PART B THE 3UCXLING WAVE PATTERN OF THIN CYLINDERS UNJ>ER COMPRESSION ---- The great disorepency between the theoretically predicted and experimentally obtained failing loads of thin walled cylinders would lead to the conclusion that some ot the as~ptions made in the theoretical treatment of the problem were not valid. One of the basic asswmptions made by all of the investigators was regarding the form of the buckling wave pattern. For this reason the authors endeavored to slow up the buckling phenomen~n so that the development of the buckles would be studied and the sizes of the initial waves measured. In order to cause buckling to take place slowly it was necessary to add the load to the cylinder head with some form of jack and applying external load enough to fail the specimen, the load being varied by the jacks. The head was then lowered by small increments and the development of the wave pattern was started. 19 APPARATUS AND !EST PROCEDURE Sinee the cylinders were made by means of a heaYy plate head and base the supporting jack was plaeed within the cylinder (~ee fig. 21). The Jack consisted of 3 set sorews which held the head of the cylinder and rested on a ! inah plate. These set screws afforded adjustment of the cylinder heed. The f inoh plate was either lowered or raised by means of three t inch diameter screws which rested on the base of the cylinder. these t inch screws being rotated by means ot a gear system. Five inch gears were placed on the • inch sorews while a two inch gear was in the center and was used as the driver. (see fig. 22). The small gear was attached to a shaft which extended through the base of the cylinder and could be turned externally by a wrench. The t inah screws were threaded with s.A.E. N. F. series and had twenty threads to the inch. The gear ratio was 2 to 5 and thus by turning the driver gear slightly a very small relative movement between the heads could be obtained. Since loads required to fail the cylinders were not over 3000 pounds, a simple loading device was set up in order that ph otogra ~hs could more easily be 20 obtained. This device (See fig 23) merely consisted of two supporting members and a cross bar. At the center of the cross bar a loading screw was placed. The specimen lay on two supporting bars in order to allow a wrench to get underneath the specimen to turn the gears. The specimen was connected to the loading screw by means of ball points with a calibrated ring in between to measure the load. The specimens used were of the same type as those discussed in the first part of this report. They were made of the same shim stock and in exactly the same manner. a fter the specimen was made, it was placed under the loading device ~nd then aligned in order to have the load vertical. Two dial gauges were placed on the specimen in such a way as to obtain the deflection. After the set screws were adjusted, a load was apglied which was beyond the failing load of the specimen dete r mined from previous tests. The head of the cylinder was slowly lowered and when buckles appeared observations were taken. The size and location of the buckle and deflection of the specimen were measured for every picture taken. Upon further lowering of t he head, the buckles would move or increase in size and at each appreciable change further data were taken . Only buckles which appeared on the side facing the camera were measured. This seemed sufficient as a good average could be obtained from one side. 21 Under this set up the thicker specimen would not show a movement of the buckles but only a sudden wrinkle pattern at failure. In some cases a few scattered wrinkle s would appear and move slightly, but even with very slow lowerping of the head the failure pattern would suddenly occur and details of its formation could not be obtained. Figures 24 and 26 represent one of the thicker specimen with an R/t of 1250 and L/R of 1.41. Thus only the one thin specimen with a thickness of .0034 inches was photographed. 22 DESCRIPTION AND COMMENTS OF BUCKLI NG PROCESS Specimen P-18 L - 9 i n. 'L/B - 1.41 t - .0034 in. R/t - 1875 Material - Steel Fie:;:re !!_ No Load Figure~ Deflection H- 0 mm. Buckle No. Lel:lBtll Circum. Height AXial in. in. 1 1/8 l 3/4 1 l l 1/.4 A B c s - .01 mm. AV • - .005 mm. Dist. From Axis Angle Position Bottom with From right Horizontal in. Deg. 2 2 3/4 3/4 45 2 0 l 0 3 These were the first buckles to form and they appeared simultaneously. Buckle A had an elliptical shape whose axis was at an angle. Buckle C was probably due to thin- nes s of the sheet at that point. seem to form any definite pattern . These two buckles do not 23 Specimen P-18 continued Figure _?1 Deflection N - Buckle No. Length Circum. Height Axial in. in. 2 l 3/4 l 1 l/4 1 l/2 l l/2 l l/.8 7/8 l l/.8 7/8 A B c D E s - .02 mm. 0 mm. Av. - .01 ~. Dist. From Axis Angle Bottom with Horizontal in. Deg. 3 2 l/2 3/4 6 3 l/2 Position from right 45 -30 0 0 45 3 l 2 2 4 New buckles formed with the existing ones becoming larger. Buckle B, with the increase in size, started to rotate its axis in conforming with the pattern which was forming on the right side of the specimen. Notice should be taken of Buckle D which has formed near the top. Buckle C has hardly changed and can be considered as local buckling due to imperfection of the sheet. All the new buckles were of elliptical shape some of whose axis were at an angle. Figure 30 Deflection Buckle No. A B c D E F N - 0 mm. Length Circum. Height Axial in. in. s - .053 mm. Av. - .0265 Dist. From A.xis Angle Position with Bottom from Right Horizontal in. Deg. 2 l l/2 l l/4 2 3/8 Has become smaller l 7/8 l 1/2 2 1 3/.8 1 1/8 1 3/4 3 2 1/2 - 45 5 5 0 30 l 1/4 - 4 30 0 3 l 2 4 5 A group of four new buckles (i') have formed to the left 24 Specimen P-18 (continued) whose size are practically equal. All their axes are at an angle and are forming a definite pattern. All the originals have increased in size with the exception of c. Buckle D has dropped and Buckle E moved to the right in forming a pattern with A and B. The axes of both A and B have rotated. Figure ,g Deflection Buckle No. A B c D E F, F..e3 4 1/ N - .015 mm. S - .143 mm. Av. - .129 mm. Length Circum. Height Axial Dist. From Bottom in. in. in. Deg. 3 1/2 4 30 0 3 1 5 5 0 15 45 30 4 6 5 2 3/.8 1 1/2 2 2 1/8 Still very small 2 2 1/2 2 1/2 2 1/.2 2 1 1/.4 2 3/8 1 3/8 4 1 - 5 Axis Angle Position with From Bight Horizontal 2 The last formed group of Buckles (F) have increased in aize forming a continuation with the pattern of the other group. !his group has shifted to the left with F , , the on e on extreme left, nearly out of the picture. Buckle A has rotated its axis while b has moved more to the right connecting with the pattern on the side of the cylinder. 25 Specimen p-18 continued Figu.re ~ Defiection Buckle llo. N - . 1 05 mm. Length Circum Height Axial in. in. s - .403 mm. A'f. - Dist. From Axis Angle Position Bottom with lt'rom Right Horizontal in. Deg. 2 3/4 3.5 0 2 3/8 Shifted i n to one coming fr om right still no change 3 0 5 3 5 0 2 7/8 2 1/2 Shifted out of picture to left 0 3 1/• 3 3 2 5/8 0 5 3 2 1/4 0 2 1/2 2 3/8 A. B c D E F 1 F 2 F 3 F 4 • 254 IJllll. fhis picture shows the whole side in failure. l 2) (1) ( 3) (4) ( 5) ( 6) The F group has now become as large as the original and there is formed the final pattern. ~he ahape with sides of equal length. buckles are of diamond The axes of all the large buckles are nearly horizontal. There are now several small buckles forming on the top end bottom similar to buckle c. 26 Comments on Specimen P-18 In the spec~en of which the picture was taken the failure first occurred at the right. deflections were not symmetrical. Thus the Likewise buckles formed first on the right and new ones for.med to the left as the load increased. It can be seen from the dimensions of the wrinkles that at first they were of elliptical shape with the maJor axis at same angle. As more load was applied there was a continual change till a failure pattern of square or diamond shaped buckles with horizontal axis was formed. Many other samples of the same thickness and length were slowly failed and observed. The final failure form seemed to be the large diamond shape inner pattern with small buckles along the edge. In most cases a single buckle was formed first due to, perhaps, some irregularity in the material. Then as more load was applied buckles formed around the original one of about the same size. They gradually 27 went into the final failure pattern as load was applied. The new buckles generally started either below or above this group and then worked up or down as the case may be until they merged into the final pattern. In many cases gmall buckles formed whioh shifted or were absorbed into the previously formed larger ones. 28 Specimen P-19 p - 19 R/t - 1870 t - .0034 l..- 6 Material - s teel s - .015 mm • Av. - .014 mm. L/R - .94 Figu.re 33 No Load Figure~ Deflection N - Buckle No. Length Circum Height Axial in. in. 2 1 7/8 2 1 7/.8 1 3/4 3/4 1 1 3/8 l l/4 l 1/4 1 1/4 3/4 A B c D E F • 013 mm. Dist. From Axis Angle Position Bottom with From Right Horizontal i n. Deg. 2 l/.4 2 3/4 2 1/4 2 3/4 2 1/4 3/4 45 5 0 4 ~5 3 2 0 45 l 6 0 All the buckles appeared at the same time. The angle of the axes alternated with adJoining buckles. The sizes were very nearly the same and they were elliptical in shape. It can be seen that the general failure pattern was formed f rom the beginni ng. Buckle F on the far lower left side was similar to Buckle C of the first specimen. Fi~re ~ s- .033 mm • Av. - . 0305 mm. Deflection N - • 028 mm. Buokle No . Length Circum. Height Axial in. in. A B c D E F l 3/4 2 2 1/8 2 3/.8 2 1/4 1 1 l/4 l 3/4 l 3/4 1 3/.8 1 3/4 1 Dist. From Axis Angle Position with Bottom From Right Horizontal in. Deg. 1 7/8 2 1/8 2 3/.8 2 3/.4 2 1/2 3/4 0 30 0 45 -45 0 5 4 3 2 1 6 The original buckles have increased in size and rotated 29 Specimen P-19 continued their axes. There are many new buckles forming between the originals of the size 1 by 1. These are making u p the links for t he fi nal form and are mainly above with a few below the originals. 36 Fi~re s - .076 mm. Deflection N - .057 mm. Buckle No. Length Circum. Height Axia l Dist. From Bottom in. in. in. Axis Angle Position with From Right Horizontal Deg. 1 3/4 1 3/8 1 3/4 1 7/8 2 1/4 1 3/4 2 7/8 1 1/2 2 1/2 1 1/2 Become small 2 1/4 2 1/2 2 1/4 2 1/2 2 l/2 30 0 -30 45 45 A B c D JS F Av. - .0665 mm. 5 4 3 2 1 The main change in this picture is the increase in size of the l a st appearing buckles to about 1 3/4 by 1 3/4. lower ones did not show much of an increase in size. The The axes of the original buckles made noticeable rotations. Fi~re Deflection N - .l05mm. Buckle No. Length Circum. Height Axi al in. in. A B c D E F l 1/2 2 1/4 2 1/4 2 1/4 2 1/4 2 1/4 2 l/4 2 l/2 2 1/2 2 l/2 Still small 37 s - • 13 mm. Av . - .1175 mm • Dist. From Axis Angle Position with From Right Bottom Horizontal in. Deg. 2 1/4 2 1/4 2 1/4 2 1/2 2 1/2 0 0 0 30 -30 5 4 3 2 1 Many new buckles were formed near the edges of the cylinder ?0 Specimen P-19 continued of about the size 1 by 1. The buckles which appeared in picture 35 above the originals have now the size of 2 1/4 by 2 1/4. ~hus they ere now of the same size and completing the failure pattern with the originals. Notice that all the larger buckles are of the same size and that the axes are nearly all horizontal. Figure 38 Deflection N - .16 mm. s - .212 mm. Av . - .186 mm. All the original buckles remained the same size with D and E becoming slightly smaller and rotating their axes to the horizontal position. ~he buckles in the top row have now formed the failure pattern with the originals. The smaller buckles which were below the originals have now been absorbed by them. There are till the smaller buckles along the edges of the cylinder. 31 C~ents on Specimen P-19 On this specimen single buckles did not for.m at first but a pattern of a whole group formed simultaneously with new ones forming as the load increased. The same phenomenon ooourred as that noted previously, that is. the waves were first elliptical and then went into a diamond or square shape. The final failure pattern was very similar to that obta ined in the longer specimen. Many cylinders of the same dimensions were failed and the wrinkle formation was similar but in the other oases, the failure pattern occurred much more rapidly and the change could not be observed as well as is shown in the photographs. 32 Specimen P-20 L - 3 t - .00 34 L/B - .47 Material - Steel R/t - 1870 Figure 39 No Load Fi~re Deneotion l>uckle No. N - 0 mm. s - .018 ma. Length Cirown. Height Axial in. in. a 1 1/4 b l 40 Av. - • 009 DUll. Dist. From Axis Angle Position Bottom with From Bight Horizontal in. Deg. 3/4 1/2 1/2 1/2 0 1 0 2 The two buckles seen in this picture are probably due to local imperfections and did not seem to effect the final failure pattern. However, the occurrence of the failur e pattern was so fast that it could not be observed if buckles a and b had any effect. 33 Specimen P-20 continued Figure 41 Buekle No. A B c D E F H I Length Height Circum. Axial in. in. 1 1/8 1 1/4 1 1 1 1/4 1 1/2 1 1/4 1 1 1/4 1 3/4 3/4 3/4 1 7/8 3/4 Dist. From Axis Angle Position Bottom with From Ri ght Horizontal in. Deg. 1 1/4 1 1/4 1 1/4 1 1/4 0 0 3/4 0 3/4 3/4 3/4 1 3 5 0 0 7 2 0 0 4 6 8 0 lfo Picture Deflection Buckle No. A B c D E F H I N - .01 mm. S - .10 mm. Av. - • 055 mm. Length Circum. Height Axial i n. in. Dist. From Axis Angle Position Bottom with From Right Horizontal in. Deg. 1 3/4 1 1{2 1 1/2 1 1/2 1 3/4 1 1/4 1 1/2 1 1 1/4 1 1/4 1 1 1/4 1 1 1 3/4 1 3/4 1 3{4 1 1/2 1 1/2 1/2 1/2 '3/4 3/4 0 0 0 1 3 0 7 2 0 0 0 0 5 4 No picture was taken as the only ehange was slight increas e in size of the buckles. 6 8 Comment s on Specimen P-20 In this case the buckles all formed simultaneously in the final failure pattern. This was also observed in the failure of other specimen of the same type. As more load was applied the movament of the buckles was slight and only an inorease in size was notioed. The buokles in this case were from the beginning not of ) elliptioal shape but of the diamond or square shape. No appreciable movement or growth of the failure pattern oould be observed in these shorter speopnen. 35 Gm{ERAL DISCUSSI ON OF RESULTS It should be noted that the shim stock used had irregularities and perhaps was the cause of singular buckles forming and disappearing. In the final failure of all the spec imens the buckles had the same pattern and shape. However the size varied slightly with the length of the specimen. Even though the radius was the same in every case, the circumferential size of the buckles was not the same at failure but varied with the length of the cylinder, that is the longer cy linders had buckles 1 with the longest circumferential. length. It can be concluded that in thin long cylinders there is a definite movement of the buckles fram its original position to final failure. However, in shorter or thicker spec imen the failure pattern appear ed to be formed almost instantaneously with little movement of buckles. However, with more refined test apparatus it might be possible to slow down the process still further so a s to obtain a gradual development of the wave form in the shorter specimens. This should probably be done in any f uture research on the problem. The results obtained so far indicate that the initial buckled state of the cylinder is ·q uite different from that assumed for previous theoretical work in the probl6m· It is hoped that this information will be of assistance in guiding future theoretical treatment so that a more accurate prediction of the critical f a iling stress of such cylinders oan be obta ined. Table 1 nominal thickness • 002 in. . 003 .004 . 005 .006 .0085 Young's liodulus 33.5 x 1cf #/in . 32.0 X lOb 32 .4 X 10'31.5 X 10~ 30 .6 X lOb 29.0 x lo6 Variations of You~'s Modulus with thickness Fi~.l Tension Test A~paratus in Reihle Testing Machine. ;a Fig .2 Cylinder Bulkhead - ? i p; .3 Assembled Cylinder / Fll$. 48 Tes t Apparatus with Specimen in Position. Fig .5 Failure of Elller Elemental Strip F1p;.6 Failure with Torsion